Preheat broiler. Lightly oil baking sheet. Slice eggplant in rounds.

Spread mayonnaise sparingly on both sides of each eggplant slice, then did the slices in grated Parmesan cheese, thoroughly coating both sides.

Arrange the slices in a single layer on the oiled baking sheet and place under broiler until golden brown, about 3 minutes. Flip the slices and broil until golden brown and crunchy on top and the eggplant is soft, about 3 minutes more.